Predicting the timing of a castrate resistant prostate cancer is critical to lowering medical costs and improving the quality of life of advanced prostate cancer patients. We formulate, compare and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). We accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). While these models are simplifications of a previously published model, they fit data with similar accuracy and improve forecasting results. Both models describe the progression of androgen resistance. Although Model 1 is simpler than the more realistic Model 2, it can fit clinical data to a greater precision. However, we found that Model 2 can forecast future PSA levels more accurately. These findings suggest that including more realistic mechanisms of androgen dynamics in a two population model may help androgen resistance timing prediction.

Background:
Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.

Results:
We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.

Conclusions:
The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.

High proportions of autistic children suffer from gastrointestinal (GI) disorders, implying a link between autism and abnormalities in gut microbial functions. Increasing evidence from recent high-throughput sequencing analyses indicates that disturbances in composition and diversity of gut microbiome are associated with various disease conditions. However, microbiome-level studies on autism are limited and mostly focused on pathogenic bacteria. Therefore, here we aimed to define systemic changes in gut microbiome associated with autism and autism-related GI problems. We recruited 20 neurotypical and 20 autistic children accompanied by a survey of both autistic severity and GI symptoms. By pyrosequencing the V2/V3 regions in bacterial 16S rDNA from fecal DNA samples, we compared gut microbiomes of GI symptom-free neurotypical children with those of autistic children mostly presenting GI symptoms. Unexpectedly, the presence of autistic symptoms, rather than the severity of GI symptoms, was associated with less diverse gut microbiomes. Further, rigorous statistical tests with multiple testing corrections showed significantly lower abundances of the genera Prevotella, Coprococcus, and unclassified Veillonellaceae in autistic samples. These are intriguingly versatile carbohydrate-degrading and/or fermenting bacteria, suggesting a potential influence of unusual diet patterns observed in autistic children. However, multivariate analyses showed that autism-related changes in both overall diversity and individual genus abundances were correlated with the presence of autistic symptoms but not with their diet patterns. Taken together, autism and accompanying GI symptoms were characterized by distinct and less diverse gut microbial compositions with lower levels of Prevotella, Coprococcus, and unclassified Veillonellaceae.